Stretching model with ik makes model bigger
Normally, scale will use global coordinates.
You want to use local coordinates.  

Tap N to bring up the properties panel.
Scale along the appropriate axis, such as Y.  

In the example, I scaled (from her view) left arm the standard way.
You can see it inflates, like you mentioned.   

Scaled her right arm using local properties instead,
along the Y-axis, so it stretches, but doesn't balloon out.



edit:  OK, in response to the BlendSwap link you posted:
I've never used that rig before.  

The website look nice, but loading in Blender gives me this:


I assume it's a version mismatch.  It's for Blender 2.74
You might need to ask the developer (nocemperor) about that.  

I would try this instead:  http://www.manuelbastioni.com/manuellab.php
because it uses a standard Blender bones rig.

Again, try to scale along one of the local axis
How to scale along the local axis of an object?

edit:  Oh, I just realized it wasn't loading fully.


It's better, but only loads Orange model, not Black or Blue.
Perhaps, because it's for an earlier ver of Blender.  

If you'd still like to use that .blend file,
the other trick you can do is add a Scale Constraint to the bone.  

Select rig > Pose Mode > click a limb.
Set it to the limits you need.  To scale along Y axis: